Communication and measurement systems often use spread spectrum modulation techniques to modify message signals for transmission in order to lower the probability of interception, reduce the peak power of the transmitted signals, allow greater channel sharing and/or improve interference rejection. Further, such systems may also use spread spectrum techniques to produce high resolution timing or ranging information, such as, for example, in global positioning systems. Spread spectrum modulation involves conversion of a relatively narrow-band message signal into a wide-band signal by multiplying it with, for example, a "pseudo-random" noise signal. In one arrangement, such as the direct sequence spread spectrum-system described herein, this involves amplitude modulation of the noise by the message.
Linear feedback shift registers (LFSR's) are typically used to produce the pseudo-random noise. An LFSR consists of N stages connected together to pass their contents forward through the register, with certain stages tapped, or connected, into a feedback path. The feedback path combines the contents of the tapped stages and feeds the combination back to one or more of the stages, to update the register.
The LFSR produces a sequence of symbols, for example, binary symbols or bits, that is periodic but appears random in any portion of the sequence that is shorter than one period. A period is defined as the longest sequence of symbols produced by the LFSR before the sequence repeats. When this pseudo-random series of symbols is modulated by the message, the result is a wide-band signal with a flat power spectrum over one period of the pseudo-random signal.
The period of the pseudo-random signal is determined by the number of stages in the shift register and by the feedback between the stages. An LFSR with "N" stages produces a signal with a period of at most 2.sup.N -1 bits. If the feedback of the LFSR is set up in accordance with an irreducible polynomial over GF(2), also referred to as a maximum length polynomial, the period of the LFSR is equal to this maximum value, 2.sup.N -1. The period can thus be made as long as desired by (i) including in the register a sufficient number of stages and (ii) combining the stages in accordance with an associated maximum length polynomial.
The pseudo-random noise is produced by first initializing the LFSR, that is, setting each of the stages of the LFSR to a predetermined state, and then shifting the LFSR to produce as the output of the last stage of the register a sequence of bits. These bits are used to produce the pseudo-random noise signal, which may, for example, have signal values of -1 and +1 for corresponding binary values of 0 and 1. This signal is then modulated by the message signal to produce a signal for transmission.
A receiver demodulates, or despreads, a received version of the transmitted signal by reversing the modulation process, i.e., combining the received signal with a locally generated replica of the noise signal to reconstruct the desired message. To reproduce the noise signal, the receiver includes an LFSR that is identical to the one in the transmitter. The LFSR in the receiver must be in the same state as the one in transmitter, and it must also be operated in synchronism with the received signal, to produce the desired message. The receiver must thus determine both the state of the LFSR and a clock phase from the received signal. To do this the receiver performs cumbersome search and acquisition operations. Once the LFSR is operating in synchronism with the received signal, the receiver must perform operations that accurately track the received signal, so that the LFSR continues to operate in synchronism with the signal.
While the foregoing operations are usually applied to messages in digital, i.e., binary form, they can also be applied to analog or continuous-valued bounded messages, for example, messages whose instantaneous values lie anywhere in the range -1 to +1.
To ensure that the receiver synchronizes to and remains in synchronism with the received signal, some prior known systems use chaotic modulation signals. Synchronization, or entrainment, is ensured in a chaotic system that is non-linear, dissipative and in which the transmitter and the receiver are coupled such that their joint Lyapunov exponent is negative.
In such a communication system the transmitter generates a chaotic noise signal and modulates this signal by the message signal to produce a chaotic signal for transmission. A receiver in the chaotic system manipulates the transmitted signal, by applying that signal to its own chaotic noise signal generator, thereby synchronizing this generator to the one in the transmitter and recovering the message. An example of such a system is discussed in U.S. Pat. No. 5,291,555 to Cuomo et al.
The noise signal produced by a chaotic system is randomly driven, because of the exponential amplification of small fluctuations. The system is not an ideal noise source, however. There can be linear correlations in the signal that lead to undesirable peaks in the power spectrum that must be filtered for optimum use of available bandwidth. Further, even after filtering to flatten the power spectrum there remain non-linear correlations, which can interfere with subsequent coders or make the system more susceptible to unintended reception.
The filters required to flatten these peaks are at best complex, and may not be realistically or economically feasible. Also, the filters required in the receiver to restore the peaks are also complex and may be infeasible. If so, the transmitter may have to transmit with reduced power, which may adversely affect the reception of the signal.
Moreover, if the receiver in the chaotic system is to synchronize to the transmitted signal within a reasonable time, the message signal cannot be too large when compared to the chaotic carrier signal. If the message signal is too small, however, the transmitted signal is comprised mainly of the chaotic carrier and bandwidth is wasted.
As in any communication system, there is a trade-off between time to synchronize, or lock, to a received signal and the robustness of the system, that is, the accuracy with which the system locks to the signal and remains locked thereafter. Known chaotic systems cannot be readily altered to change in a predictable way their attractor dimensions, i.e., the usable numbers of degrees of freedom. These systems thus cannot readily alter the trade-off between time to lock and robustness.